Question

Assume an investment's starting value is Rs. 10,000 and it grows to Rs. 60,000 in 4 years, then the CAGR % of the investment is,
[given : \((6)^{1/4}=1.565\)]

• A. 65%
• B. 56.5%
• C. 65.5%
• D. 55.6%

Hint:

CAGR \(=\left(\frac{60000}{10000}\right)^{1/4}-1=6^{1/4}-1\).

Answer 1

The Correct Option is B

Step 1: Understand CAGR:
CAGR stands for compound annual growth rate. It is the single yearly growth rate at which the starting value would grow to the final value over the given years.

Step 2: Recall the formula:
\[ \text{CAGR}=\left(\frac{\text{Final value}}{\text{Initial value}}\right)^{1/n}-1 \]
where \(n\) is the number of years.

Step 3: Put in the numbers:
Here the initial value is 10,000, the final value is 60,000 and \(n=4\).
\[ \frac{60000}{10000}=6 \]
\[ \text{CAGR}=6^{1/4}-1 \]

Step 4: Use the given value:
The question gives \(6^{1/4}=1.565\). So \[ \text{CAGR}=1.565-1=0.565 \]
In percent, this is \(0.565\times100=56.5\%\).

Step 5: Check the options:
Options 1 (65%) and 3 (65.5%) come from mixing up the digits. Option 4 (55.6%) is a digit swap too. Only 56.5% matches 0.565.

Final Answer:
The CAGR is 56.5%, which is option 2. \[ \boxed{56.5\%} \]